The 23-year-old joined Chelsea in 2007, where he graduated through the academy and has been a first-team player since the start of the 2021-22 season.
While he played in every match during Frank Lampard’s spell as caretaker manager, he was used more sporadically throughout the course of the whole season.
Standard Sport understands Inter are accelerating their efforts to sign the centre-back and are in communication with Chalobah’s camp on a daily basis.
It remains to be seen whether incoming Chelsea manager Mauricio Pochettino wants Chalobah to be part of the new project in west London, but it is understood Chalobah is desperate to be playing regular football with an eye on selection for England at Euro 2024.
Chalobah, who is yet to be called up to the senior squad by Gareth Southgate, is valued by Chelsea at around £25million, which is a fee Inter would be willing to part with.
The Champions League finalists play with a back three and are hoping to freshen up their ageing defence, with Matteo Darmian (33) and Francesco Acerbi (35) both in the autumn of their careers.
Inter see Chalobah as an ideal fit for their style of play and are eager to discover whether Pochettino is willing to sell the former England youth international.
Inter were interested in securing Chalobah on loan last summer, but approaches for the defender were blocked by Chelsea.
Chalobah signed a Chelsea contract extension until 2028 with an option for a further year in November, but the defender remains keen for regular football and Inter remain keen on signing him.